Hybrid flows comprising both turbidity current and submarine debris flow are a significant departure from many previous influential models for submarine sediment density flows. Hybrid beds containing cohesive debrite and turbidite are common in distal depositional environments, as shown by detailed observations from more than 20 modern and ancient systems worldwide. Hybrid flows, and cohesive debris flows more generally, are best classified in terms of a continuum of decreasing cohesive debris flow strength. High-strength cohesive debris flows tend to be clast rich and relatively thick, and their deposit extends back to near the site of original slope failure. They are typically confined to higher gradient continental slopes, but may occasionally form megabeds on basin plains, in both cases overlain by a thin turbidite. Intermediate-strength cohesive debris flows typically contain clasts, but their deposits may be <1 or 2 m thick on low-gradient fan fringes, and are encased in turbidite sand and mud. Clasts may be far-traveled, and meter-sized clasts can be rafted long distances across very low gradients if they are less dense than surrounding flow. Low-strength cohesive debris flows generally lack mud clasts, and as cohesive strength decreases further there is a transition into fluid mud layers that do not support sand. Intermediate- and low-strength cohesive debrites are consistently absent in more proximal parts of submarine systems, where faster moving sediment-charged flows are more likely to be turbulent. Intermediate-strength debris flows can run out for long distances on low gradients without hydroplaning. Very low strength cohesive debris flows most likely form through late-stage transformations near the site of debrite deposition, and emplaced gently to avoid mixing with surrounding seawater. The location and geometry of cohesive debrites in hybrid beds are controlled strongly by seafloor morphology and small changes in gradient. Debrites occur as fringes around raised channel-levee ridges, or in the central and lowest parts of basin plains lacking such ridges. Small variations in mud fraction produce profound changes in cohesive strength, flow viscosity, permeability, and the time taken for excess pore pressures to dissipate that span multiple orders of magnitude. Reduction in flow speed can also cause substantial increases in viscosity and yield strength in shear thinning muddy fluids. Small amounts of sediment can dampen or extinguish turbulence, especially as flow decelerates, affecting how sediment is supported or deposited. This ensures that cohesive debris flows and hybrid flows have a rich variety of behaviors.